Question

The sum of circumference and diameter of a circle is 145 cm, find the diameter of the circle.

Answer 1

Hint: First of all, consider the radius of the given circle as a variable. Then equate the sum of its circumcircle and diameter to 145 cm to get the value of the radius of the circle. Hence, we can obtain the diameter of the circle as it is equal to twice the length of the radius.

Complete step-by-step solution -
Let the radius of the circle be \[r\] cm as shown in the figure:

Given the sum of the circumference and its diameter = 145 cm
We know that the circumference of a circle with radius \[r\]cm is given by \[2\pi r\] cm and diameter of the circle is twice that of its radius.
So, we have
\[
  2\pi r + 2r = 145 \\
  2 \times \dfrac{{22}}{7} \times r + 2r = 145 \\
  r\left( {\dfrac{{44}}{7} + 2} \right) = 145 \\
  r\left( {\dfrac{{44 + 14}}{7}} \right) = 145 \\
  r\left( {\dfrac{{58}}{7}} \right) = 145 \\
  r = 145\left( {\dfrac{7}{{58}}} \right) \\
  \therefore r = 17.5{\text{ cm}} \\
\]
As diameter is twice that of the radius, length of the diameter \[ = 2 \times 17.5 = 35{\text{ cm}}\]
Thus, the length of the diameter is 35 cm.
Note: The circumference of a circle is the distance around the outside of the circle. And the circumference of a circle with radius \[r\]cm is given by \[2\pi r\] cm and diameter of the circle is twice that of its radius.